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Nine identical machines, each working at the same constant r
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18 Jun 2018, 14:53
18 Jun 2018, 14:53
Expert Reply
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Question Stats:
95% (01:10) correct
4% (02:08) wrong based on 67 sessions
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Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
Re: Nine identical machines, each working at the same constant r
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26 Jun 2018, 09:36
26 Jun 2018, 09:36
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sandy wrote:
Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
We know
Work = Rate * *NO. of workers * Time
So work = 27 jerseys
No. of Workers = 9 machine
Time = 4 minutes
therefore we have ;
27 = Rate * 9 * 4
So Rate = \(\frac{3}{4}\) jersey/minute
Now we need to find the time required to make 60 jersey with 4 machine
SO;
Work = Rate * *NO. of workers * Time
Now work = 60 jerseys
Rate = \(\frac{3}{4}\) jersey/minute
No. of workers = 4 machine
Therefore;
60 = \(\frac{3}{4}\) * 4 * Time
or Time = 20 minutes
Re: Nine identical machines, each working at the same constant r
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10 Jul 2018, 05:27
10 Jul 2018, 05:27
Expert Reply
Explanation
To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Solve for an individual machine’s rate, using the fact that 9 machines can stitch 27 jerseys in 4 minutes:
Work = Individual Rate × Number of Workers × Time
27 jerseys = (R)(9)(4 minutes)
R = \(\frac{3}{4}\) jersey per minute
That is, each machine can stitch \(\frac{3}{4}\) of a jersey in 1 minute. Plug that rate back into the formula, but using the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(6 = \frac{3}{4} (4)(T)\)
T = 20
To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Solve for an individual machine’s rate, using the fact that 9 machines can stitch 27 jerseys in 4 minutes:
Work = Individual Rate × Number of Workers × Time
27 jerseys = (R)(9)(4 minutes)
R = \(\frac{3}{4}\) jersey per minute
That is, each machine can stitch \(\frac{3}{4}\) of a jersey in 1 minute. Plug that rate back into the formula, but using the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(6 = \frac{3}{4} (4)(T)\)
T = 20
